How many stereoisomers of `(CH_(3) )_(2) CHCH= CHCH_(2) CH(OH) CH_(2) Br` are possible

Options

A. 2
B. 3
C. 4
D. 5

Answer

To determine the number of stereoisomers for the compound `(CH₃)₂CHCH=CHCH₂CH(OH)CH₂Br`, we will follow these steps:

### Step 1: Identify the Stereocenters
A stereocenter (or chiral center) is a carbon atom that is bonded to four different groups. In the given compound, we need to analyze the structure to find such carbon atoms.

1. **Draw the Structure**:
- The compound can be represented as:
```
CH₃
|
CH₃-C-CH=CH-CH₂-CH(OH)-CH₂Br
```
- Identify the carbon atoms in the chain and check for chirality.

2. **Count the Stereocenters**:
- In this structure, we can identify the following stereocenters:
- The carbon with the hydroxyl group (OH) is a stereocenter because it is attached to different groups (Br, H, CH₂, and the rest of the carbon chain).
- The carbon adjacent to the double bond (C=C) can also be a stereocenter if it has different substituents.
- After analyzing, we find that there are **2 stereocenters** in this compound.

### Step 2: Determine the Number of Stereoisomers
To find the number of stereoisomers, we use the formula:
\[ \text{Number of stereoisomers} = 2^n \]
where \( n \) is the number of stereocenters.

1. **Apply the Formula**:
- Here, \( n = 2 \).
- Therefore, the number of stereoisomers is:
\[ 2^2 = 4 \]

### Conclusion
The total number of stereoisomers for the compound `(CH₃)₂CHCH=CHCH₂CH(OH)CH₂Br` is **4**.

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